Question

resolva a equação de 2° grau (fórmula completa):

2x² - x - 3 = 0

ficaria agradecido pela resposta.​

Answer 1

$\large\displaystyle \mathsf{2x^2-x-3=0}$

$\large\displaystyle\text{ \mathsf{ \begin{cases}\sf a=2\\\sf b=-1\\\sf c=-3\end{cases} } }$

$\large\displaystyle \mathsf{ \Delta=b^2-4\cdot a\cdot c }$

$\large\displaystyle \mathsf{ \Delta=(-1)^2-4\cdot 2\cdot (-3) }$

$\large\displaystyle \mathsf{ \Delta=1+24}$

$\large\displaystyle \mathsf{\Delta=25 }$

$\large\displaystyle\text{ \mathsf{ x=\dfrac{-b\pm\sqrt{\Delta}}{2\cdot a}} }$

$\large\displaystyle\text{ \mathsf{ x=\dfrac{-(-1)\pm\sqrt{25}}{2\cdot2}} }$

$\large\displaystyle\text{ \mathsf{x=\dfrac{1\pm5}{4} \begin{cases}\sf x_1=\dfrac{1+5}{4}=\dfrac{6^{\div2}}{4^{\div2}}=\dfrac{3}{2}\\\\\sf x_2=\dfrac{1-5}{4}=\dfrac{-4}{4}=-1\end{cases}} }$